IEEE Access (Jan 2018)

On the Metric Dimension of Generalized Petersen Multigraphs

  • Muhammad Imran,
  • Muhammad Kamran Siddiqui,
  • Rishi Naeem

DOI
https://doi.org/10.1109/ACCESS.2018.2883556
Journal volume & issue
Vol. 6
pp. 74328 – 74338

Abstract

Read online

In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by $P(2n,n)$ have metric dimension 3 when $n$ is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs.

Keywords